Given a maximal subgroup \(M\)  of a group \(G\) , the quotient \(G/M_G\)  of
\(G\)  by the normal core \(M_G\)  of \(M\)  in \(G\)  is a primitive group. According
to a well-known theorem of Baer [1]} (see also
[2]}), \(G/M_G\)  is of one of three
different
types. In this case, we say that the maximal \(M\)  is of the same type as
the primitive group \(G/M_G\)  it induces, like in
[2]}. Lubotzky [4]} established bounds on the number of maximal subgroups of type 1 of a given index \(n\)  and on the number of maximal subgroups of types 2 and 3 of index \(n\)  by considering the number of abelian and non-abelian chief factors, respectively, in a given chief series of the group. He obtained the following result that confirms the validity of Pak's conjecture.
